In the game Hot Potato, each player starts with 100 points. One unlucky player, chosen at random, is initially given the hot potato. On each turn, the player with the hot potato decides which player gets it next, and the recepient's score is decremented by one. The hot potato may not be passed to a player with a score of zero. The winner is the last player with a positive score.

I cannot fathom any coherent strategy for Hot Potato. How to approach it formally is a complete mystery to me.

Second Best

In the game Second Best, each player writes down a word and then all words are revealed. All players who wrote down the second most commonly occuring word are winners, everybody else are losers. In the case of a tie for second, everybody loses.